Application of RRT Algorithm in Obstacle-Free Toroidal Space

The Rapidly-exploring Random Tree (RRT) algorithm is a path search algorithm that utilizes random sampling and tree structure expansion, enabling rapid exploration of high-dimensional spaces. As a result, it is widely applied in the field of robot path planning as a sampling algorithm. However, the traditional RRT algorithm is primarily used in Euclidean spaces, and its application in non-Euclidean spaces, such as toroidal spaces, has been relatively less studied. This paper explores the application of the RRT algorithm in obstacle-free toroidal spaces, analyzing its sampling methods for sampling points, distance metrics for tree nodes, and the expansion of the tree structure within such spaces, so the TOF-RRT (Toroidal Obstacle-Free Rapidly-exploring Random Tree) method is introduced in this study. The TOF-RRT method has been validated through numerical simulations, demonstrating its effectiveness in solving path planning problems in obstacle-free toroidal spaces.